Yarn winding apparatus barrel cam and method of making the cam groove

ABSTRACT

A yarn winding apparatus for winding generally cylindrical cross-wound packages in which the yarn wave in the extremity of each reversal has the smallest possible radius it will retain on the package. The apparatus includes a rotatably driven barrel cam having a generally continuous helical groove in its surface, a traverse guide riding in the groove through which yarn passes at an angle in an uncontrolled length to a point of tangency on a driven cylinder spaced from the guide. The groove has a profile comprising successive helical, reversal curve and helical portions. The reversal curve portion is characterized by being derived from the sum of the first derivative of the yarn reversal plus the product of the uncontrolled yarn length and the second derivative of the yarn reversal curve. The yarn package comprises layers of helical coils wound on a bobbin. The coils are laid down at the mid-portion of their reversals throughout the package in a curve having a minimum radius R according to the expression:

United States Patent Ake'rs et al.

[54] YARN WINDING APPARATUS BARREL CAM AND METHOD OF MAKING THE CAM GROOVE [72] lnventorsz Richard L. Akers, Wilmington, .Del.;

[73] Assignee:

22 Filed:

Donald W. Oplinger, Lynnfield, Mass.

E. I. du Pont de Nemours and Company, Wilmington, Del.

Feb. 11, 1970 [21] Appl. No.: 10,493

Primary ExaminerStanley N. Gilreath Attorney-Howard P. West, Jr.

[ 1 July 11,1972

[5 1 Answer A yarn winding apparatus for winding generally cylindrical cross-wound packages in which the yarn wave in the extremity of each reversal has the smallest possible radius it will retain on the package. The apparatus includes a rotatably driven barrel cam having a generally continuous helical groove in its surface, a traverse guide riding in the groove through which yarn passes at an angle in an uncontrolled length to a point of tangency on a driven cylinder spaced from the guide. The groove has a profile comprising successive helical, reversal curve and helical portionsv The reversal curve portion is characterized by being derived from the sum of the first derivative of the yarn reversal plus the product of the uncontrolled yarn length and the second derivative of the yarn reversal curve. The yarn package comprises layers of helical coils wound on a bobbin. The coils are laid down at the mid-portion of their reversals throughout the package in a curve having a minimum radius R according to the expression:

where r is the radius of the bobbin andu is the coefficient of friction of the yarn.

5 Claims, 7 Drawing figures PKTEN'TEDJuLmsn 1 3.675863 SHEET10F3 FIG-Z TRAVERSE wEC ION INVENTORS RICHARD L. AKERS DONALD -W.- OP LINGER v BY ATTORNEY PKTENTEDJUL 11 I972 3.675.863 sum 20F a F l G. 4

INVENTORS RICHARD L. AKERS DONALD W. OPLINGER ATTORNEY 'PATENTEDJummz 3,675,863

sumanr 3 I PROGRAM OF CAM DISPLACEMENT N REVERSAL INVENTORS RICHARD L. AKERS DONALD W. OPLINGER.

ATTORNEY YARN WINDING APPARATUS BARREL CAM AND METHOD OF MAKING THE CAM GROOVE BACKGROUND OF THE INVENTION This invention relates to a traversing cam means and, more particularly, to a cam reversal for controlling the laydown behavior of filamentary materials during the high speed winding of a generally cylindrical, flat-ended cross-wound package on a rotatable tubular support.

It has been a practice in designing cams for windups to attempt to program the rate of traversing of the advancing yarn, particularly in the reversal regions, in such a way as to control the shape of the ends as well as the peripheral surface of packages being wound. For example, corrective measures in reversal rate have been tried in an effort to avoid raised shoulders, soft regions, overthrown ends, bulging and other defects. Tending to aggravate the problems is high speed operations, e.g., 3,000 yarns per minute yarns speed and higher because increases in inertia forces in the traverse mechanism then impose further limitations on the kinds of reversals that may be used. The corrective measures used have been concerned primarily with cam design permitting rapid reversal without subjecting the cam and follower to excessive loads at the cam reversal points and generally are of a trial and error nature, e.g., a desired yarn wave shape is approximated in a series of test cams with successive groove alterations followed by test packages until a cam produces a desired package. Furthermore, the distortion introduced in the actual yarn laydown pattern by the uncontrolled yarn length between the traverse guide and the print roll or package has been essentially ignored. Thus, despite the improvements provided by the use of such devices as cam cutback, as taught by Chaussy in US. Pat. No. 3,089,657, some undesired variations in package profile or shape and other defects nevertheless were still present.

SUMMARY OF THE INVENTION It is an object of this invention to provide a barrel cam having a reversal formed in accordance with a calculated relationship existing between the yarn wave shape contemplated and the groove in the cam. The cam functions in a winding apparatus and has a generally continuous helical groovein its surface. A traverse guide rides in the groove and yarn passes through the guide in an uncontrolled length to a point of tangency on a driven cylinder spaced from the guide. The groove has a profile that includes successive helical, reversal curve and helical portions. The reversal curve exhibits a specific mode of displacement, designed to be in conformity with and have the capability of forming, in conjunction with a windup apparatus, a yarn package reversal wave exhibiting the sharpest curvature which the yarn will retain with consistency based on yarn properties and characteristics per se and upon behavior of the yarn relative to its environs. The yarn package has an optimum yarn reversal which is defined as one which will give rise to the least possible package shoulder buildup with substantially a complete absence of overthrown ends. The yarn may be laid down on adrive roll and subsequently on a package or directly on the package and is characterized by a yarn wave shape in the reversal regions which has the sharpest (or least) radius of curvature that the yarn will accept and retain, temporarily. The yarn reversal region has a mid-portion of about 50 percent of the reversal length which is a curve having a radius that varies less than 10 percent from a mean value. The reversal regions are further characterized by a yarn wave shape in substantially any one of the reversals which,

taking increments of yarn displacement in the direction of.

traverse and differentiating twice relative to increments of displacement at 90 thereto, yields when plotted on rectangular coordinates a generally square curve having'corners which are not aligned with the peak of the yarn reversal, that is, the point of nearest approach of the yarn to the nominal end of the package. All points of the generally square curve for not less than 50 percent of its extent measured circumferentially of the package have a height measured from the zero value line of at least percent of the maximum height of the same curve. The term curvature that the yarn will accept and retain, temporarily" means that the filamentary material being wound (or curved) takes no permanent deformation or crimp and upon being backwound from the package will hang substantially straight by its own weight. By nominal end of package is meant the generally planar or slightly conical or oblate conical end face of the wound package the surface of which one sees upon viewing the package end.

BRIEF DESCRIPTION OF THE DRAWINGS I FIG. 1 is a side elevation of a winding apparatus in which the present invention may be used.

FIG. 2 is a developed view of the surface of the drive roll of FIG. 1 showing the path of the yarn as it is deposited on the roll.

FIG. 3 is a diagrammatic view along line 3-3 and from behind the cam of FIG. 1.

FIG. 4 is a top plan view of a barrel cam having groove with a profile representative of those of this invention.

FIG. 5 represents a developed view of the yarn reversal obtained with this invention.

FIG. 6 represents a rectangular plot of the second derivative of the yarn reversal of FIG. 5.

FIG. 7 represents the program of cam displacement derived of a cam groove such as shown in FIG. 4.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT The present invention will be described in relation to a windup apparatus of the type shown in FIGS. land 4 which comprises a frame 13 carrying a cam assembly 10 and a fixed drive roll 5 coupled to a motor 6. A bobbin 7 is situated on a support 8 which is carried on a pivoted arm 9 which is adapted to urge the bobbin 7 or the growing package 2 against the drive roll 5. A typical cam apparatus 10 generally comprises a barrel cam l on a shaft 11 mounted for rotation in bearings in fixed pedestals 20 to which aresecured spaced, parallel guide rails 4 which hold a cam follower-traverse guide 33 in engagement with a cam groove 14 in the barrel'cam 1 thus being adapted to'traverse yarn 15 asit advances from a fanning guide 16 toward the drive roll .5 and thence to the package 2.

The yarn is swept back and forth in a zig-zag pattern shown in the developed view, FIG. 2, and is deposited temporarily on the peripheral surface 12 of the drive roll 5 which is moving downward in the direction of the arrow 18. The drive roll carries the yarn to the point of tangency with the bobbin 7 or package 2 where the yarn, substantially in the configuration in which it was laid down, is deposited or printed" on the surface of the package 2. It may be seen that the yarn is laid down in helical paths as represented by straight line portions 24 and in curving reversal regions 17. This invention is concerned with the shape and behavior of the yarn line in these regions 17. In FIG. 1 the width of the guide 33 plus the need for operating clearance in respect to the surface of the drive roll 5 or package 2 means that there is a lower limit on the distance measured from the guide 33 perpendicularly to a line parallel to the drive roll axis through the point of tangency 19 of the yarn on the drive roll. This distance is called the uncontrolled yarn length and is designated by the letter U. In practical windups U may be about 0.3 toabout 0.9 inch, but may be as great as two inches. It is common to keep this length U to a practical minimum because of its influence on package length (i.e., as U becomes longer, the package becomes shorter), but more particularly, because of its influence on the shape of the yarn curve as it is laid on the drive roll, the effect being most pronounced and of most significance in the reversal regions 17. Generally, the yarn on a given point of tangency with the drive roll 5 will lag behind the instantaneous position of the traverse guide 33 in the reversal regions. The amount of this lag is continuously variable and tends to blur or distort the yarn path from the shape desired or the shape predicted based solely on cam displacement. If the windup is viewed along line 33 in FIG. 1 from behind the cam l, the diagrammatic view of FIG. 3 may be visualized. Yarn 15 is being traversed to the left by means of the traverse guide 33 which is moving at a velocity V according to a program defined by curve 30. The yarn is being laid on the surface 12 of the drive roll at point of tangency (or laydown) 19. Since the yarn lags behind the traverse, the uncontrolled yarn is disposed at an angle A across a distance U. The relative position of the traverse guide 33 or the locus of curve 30 may be taken as y, measured from a reference line 31 which is situated at right angles to the direction of traverse while the corresponding instantaneous position of the point of tangency 19 of the yarn on the drive roll, designated y, is measured from the same line 31, then, assuming no yarn slippage at the point of yarn laydown and negligibly small yarn inertia effects in the uncontrolled expanse, the following equation may be written:

andy,=y+U(tanA) (l) but since tan A dy/dx the instantaneous slope of the yarn curve (1: being the displacement of the curve 30 in the same direction as the motion of the drive roll surface as indicated by arrow 18 and measured parallel to line 31), substitution may be made, thus:

y=y+ y/ x) (2) Differentiating, we get:

ytldx dy/ x U y/M) (3) This is the equation which relates the shape of the traverse function, or the program of cam displacement, to the shape of the yarn wave on the package.

In constructing a cross-wound yarn package most nearly approaching perfection it is necessary that the yarn lie in purely helical paths, or, in other words, if a perfect package could be made each increment of its length would contain precisely the same amount of yarn as any other increment of like length measured axially. Carried to the ends of the package, this means that each of the reversal regions would comprise two intersecting helices with a zero radius at the reversal. It should be realized, however, that such a state of perfection as represented by two intersecting helices is virtually impossible to attain.

Recognizing that any practical reversal is less than perfect, an ideal yarn reversal shape, the one which most nearly conforms to purely helical paths approaches one which is completely symmetrical relative to the reversal and one which at the peak of the actual yarn reversal and throughout the reversal exhibits the greatest curvature (minimum radius) which the yarn will accept and retain with stability while on the package. Further, according to this invention, the cam shape in the reversal is arrived at by considering the yarn shape contemplated rather than vice-versa. The minimum radius R sustainable by the yarn is defined by the expression:

R r/u (4) where r is the radius of a cylinder on which the yarn is to be deposited and u is the coefficient of static friction of the yarn on said cylinder. It will be recognized that the behavior of the yarn should be checked for all cylindrical surfaces encountered to determine minimum radius R. In a practical system r is fixed and may be about 1 inch with u being in the range of about 0.05 to about 0.22, therefore, R may range from about 20 to about 4.5 inches. R is used to establish the optimum value of the second derivative of a desirable yarn reversal curve, as will be explained later.

Since, according to the present invention, it is desired to deposit yarn on a package substantially in an arcuate form of minimum radius through a maximum portion of the reversal,

this basic criterion is used as a starting condition for the design of a yarn wave and then of a traversing cam as detailed below. In the discussion of the effect of uncontrolled yarn length U it was shown that the shape of the traverse program is related to the yarn path according to the Equation (3) Thus, it is not only necessary to look at the slope of the desired arcuate yarn path but it is necessary to consider the values of the second derivative as well.

An enlarged representation of yarn reversal region 17 is shown in FIG. 5 where it can be seen that the truly helical portions 24 of the path merge into the true arcuate portion 26 through merge regions 25.

A plot of the second derivative of a yarn path similar to that represented by FIG. 5 is shown in FIG. 6 wherein the merger from helical portions to arcuate portions is represented by S- shaped curves 27 which are faired into the abscissa and end portions of 23a with identically equal slopes at merge points. These S-shaped curves 27 may have substantially any shape such as harmonic, cycloidal or polynomial but truly arcuate shapes are to be avoided. In actual designs the principal criteria for selecting and fitting the S-shaped curves in the yarn path second derivative plot are: (1) that merging curves have identically equal slopes and (2) that the extent of the curves, measured horizontally (along the abscissa) should not be too short (to avoid high rates of acceleration in the cam follower and/or excessive pressure angles) nor too long (to avoid excessive intrusion into either the helical portion or the reversal portion of the cam).

A curve such as that of FIG. 6 is used to determine the shape of the program of cam displacement 32 which appears generally as shown in FIG. 7. Superimposed on this is a representation of the curving reversal region (of FIG. 5) and a comparison of these curves reveals that the uncontrolled yarn length U introduces a considerable disparity between yarn displacement and cam displacement. This, of course, emphasizes the need for designing the cam shape from the yarn reversal desired instead of vice-versa. The program of cam displacement is computed and plotted by employing values for the first and second derivatives of the yarn path in Equation (3). This program of cam displacement is used to compute coordinates of a cam groove 14 such as illustrated in FIG. 4.

As will be noted from Equation 3), in order to arrive at a cam displacement program, it is not only necessary to know a succession of values of the second derivative but also the corresponding successive values of the first derivative as well. Thus, to find the first derivative, integration is carried out and must be done in small increments of x measured along the abscissa of the second derivative plot (FIG. 6). If desired, this may be done manually, for example, taking the recess side of the second derivative plot, (the maximum value of which is, say 0.l3) and a small increment of 2:, say Ax 0.05 inch, then the area of the rectangle 39 is (0.13) (0.05) .0065 This value taken as ordinate may be plotted with Ax as abscissa. Similarly, a succession of increments, Ax each 0050 wide, may be taken to find successive areas which when added to each other sequentially result in a curve which shows successive values of the slope dy/dx of the yarn curve.

Although as noted above the calculations incident to this procedure may be carried out manually, it is more convenient to use a computer which may be programmed to calculate the values. At this stage, since a table of values of d y/4x and corresponding values of dy/dx are known, substitution may be made in Equation (3) to find successive values for dyildx the shape of the traverse function, which values may be used in the design of an actual cam by effecting an affine transformation (Mathematics Dictionary, 3rd Edition, pages 6-7, D. Van Norstrand Co., Inc.). Thus, in essence, the program for one entire traverse cycle (assuming the actual cam is to make I revolution per traverse cycle) must be compressed" to fit around the periphery of the barrel cam thus establishing cam groove coordinates used to form a closed loop in which the cam groove is endless." This usually means that the helix angle on the cam generally called the pressure angle is a great deal greater than the desired helix angle on the yarn package. In some cases the cam groove helix angle becomes so large that an inoperable pressure angle (cam groove Vs. cam follower) is reached which can be cured (a) by making the cam stroke shorter, (b) by increasing the diameter of the cam barrel or (c) by changing the cam so as to have a plurality of revolutions per traverse cycle thus introducing intersections or crossovers in the cam grooves. When the cam groove coordinates have been established, they are used to compute the first and second derivative (for the non-helical portions) to determine whether cam follower accelerations fall within acceptable limits.

As can be seen from an actual plot of a second derivative (FIG. 6) the second derivative of the yarn curve described is generally trapezoidal in shape and H is about 85 percent of H and K is about 52 percent of k This embodiment falls within the scope of the invention, i.e., the second derivative is a line within the reversal region in which all points along the line for not less than 50 percent of its extent measured along the time axis have a height measured from the zero value line of at least 85 percent of the maximum height of the same line.

When the above conditions are met, it is found that the radius of curvature of the yarn reversal does not vary appreciably (i.e., less than :t percent) from the mean radius (in the same portion). More specifically, on a large number of yarn paths and cams falling within the scope of the present invention, this radius of curvature varied by less than plus and minus 0.5 inch from the mean across at least 50 percent of the reversal length. This is in marked contrast to yarn paths determined by prior art cams which, when subjected to mathematical analysis as detailed herein, showed variations of at least plus and minus 1.9 inches in radius of curvature of yarn across only the central one-third of the reversal (vs. 50 percent of the reversal for the present invention) or a variation in radius almost four times as great as in the present invention.

The actual radii of curvature K may be determined by the Since values for the first and second derivative of the yarn path are known, the calculation of the radius of curvature K is easily carried out. The minimum radius of curvature R as defined in equation 4 will be seen to be equal to K when the slope of the yarn reversal curve dy/dx becomes zero and will equal the negative reciprocal of the second derivative. From this it will be seen that the reciprocal of R calculated in Equation 4 is a guideline for the selected value of the second derivative.

In practical windup cam reversals, the optimum value of the second derivative dy/dx at the peak of reversal as derived from Equations 3 and 4 will be about 0.14 to 0.15 for package helix angles of about 102, 0.1 l to 0.13 for package helix angles of l 1.7 and 0.09 for package helix angles of l6". The optimum values of 0.l l to 0.13 have been found to be useful in winding 6-6 nylon trilobal yarn, 40-13 count at a winding tension of about 7.5 grams in a range of helix angles of about 107 to ll.7 on different packages. The cams used for these windings were designed for an 1125 helix angle and a minimum yarn radius at the peak of the reversal of 7.69 inches.

Use of the cams of this invention permits winding at higher helix angles without the usually accompanying defects of overthrown ends and spiral fans, minimizes shoulder buildup, and provides packages with lower bulge.

What is claimed is:

l. A yarn winding apparatus for winding generally cylindrical cross-wound yarn packages wherein the yarn is laid down at its reversal in a curve having a minimum radius R according to the expression where r is the radius of a cylinder on which the yarn is deposited and u is the coefficient of friction of the yarn, said apparatus including a rotatably driven barrel cam having a generally continuous helical groove in its surface, a traverse guide riding in said groove through which yarn passes at an angle in an uncontrolled length to a point of tangency on a driven cylinder spaced from said guide, the improvement comprising: said groove having a profile comprising successive helical, reversal curve and helical portions, said reversal curve having a shape derived from the product of said uncontrolled length and the second derivative of the yarn reversal curve.

2. The apparatus as defined in claim 1, said second derivative of said yarn reversal curve being of substantially constant value throughout about 50 percent of the yarn reversal.

3. The apparatus as defined in claim 1, said minimum radius R having a variation of less than 10 percent through about 50 percent of said reversal.

4. The apparatus as defined in claim 1, said uncontrolled length being in the range of from about 0.3 to 0.9 inch and R being in the range of from about 4.5 to about 10 inches.

5. A yarn winding apparatus for winding generally cylindrical cross-wound yarn packages wherein the yarn is laid down for about 50 percent its reversal in a curve having a minimum radius R according to the expression:

R r/u where r is the radius of a cylinder on which the yarn is deposited and u is the coefficient of static friction of the yarn on said cylinder, said apparatus including a rotatably driven barrel cam having a generally continuous helical groove in its surface, a traverse guide riding in said groove through which yarn passes at an angle in an uncontrolled length to a point of tangency on a driven cylinder spaced from said guide the improvement comprising said groove having a profile comprising successive helical, reversal curve and helical portions, said reversal curve having a shape derived in accordance with the sum of the first derivative of the yarn reversal curve plus the product of said uncontrolled length and the second derivative of the yarn reversal curve, the second derivative of the yarn reversal curve being generally trapezoidal. 

1. A yarn winding apparatus for winding generally cylindrical cross-wound yarn packages wherein the yarn is laid down at its reversal in a curve having a minimum radius R according to the expression R r/u where r is the radius of a cylinder on which the yarn is deposited and u is the coefficient of friction of the yarn, said apparatus including a rotatably driven barrel cam having a generally continuous helical groove in its surface, a traverse guide riding in said groove through which yarn passes at an angle in an uncontrolled length to a point of tangency on a driven cylinder spaced from said guide, the improvement comprising: said groove having a profile comprising successive helical, reversal curve and helical portions, said reversal curve having a shape derived from the product of said uncontrolled length and the second derivative of the yarn reversal curve.
 2. The apparatus as defined in claim 1, said second derivative of said yarn reversal curve being of substantially constant value throughout about 50 percent of the yarn reversal.
 3. The apparatus as defined in claim 1, said minimum radius R having a variation of less than 10 percent through about 50 percent of said reversal.
 4. The apparatus as defined in claim 1, said uncontrolled length being in the range of from about 0.3 to 0.9 inch and R being in the rAnge of from about 4.5 to about 10 inches.
 5. A yarn winding apparatus for winding generally cylindrical cross-wound yarn packages wherein the yarn is laid down for about 50 percent its reversal in a curve having a minimum radius R according to the expression: R r/u where r is the radius of a cylinder on which the yarn is deposited and u is the coefficient of static friction of the yarn on said cylinder, said apparatus including a rotatably driven barrel cam having a generally continuous helical groove in its surface, a traverse guide riding in said groove through which yarn passes at an angle in an uncontrolled length to a point of tangency on a driven cylinder spaced from said guide the improvement comprising said groove having a profile comprising successive helical, reversal curve and helical portions, said reversal curve having a shape derived in accordance with the sum of the first derivative of the yarn reversal curve plus the product of said uncontrolled length and the second derivative of the yarn reversal curve, the second derivative of the yarn reversal curve being generally trapezoidal. 